Related papers: On the Sequential Multiknapsack polytope
We study relationship among versions of the Knapsack Problem where variables take values in Z and the number of them is fixed. In particular, we construct a finitely presented group where the problem of solvability of exponential equations…
Multi Expression Programming (MEP) is a Genetic Programming variant that uses linear chromosomes for solution encoding. A unique feature of MEP is its ability of encoding multiple solutions of a problem in a single chromosome. In this paper…
In the incremental knapsack problem ($\IK$), we are given a knapsack whose capacity grows weakly as a function of time. There is a time horizon of $T$ periods and the capacity of the knapsack is $B_t$ in period $t$ for $t = 1, \ldots, T$.…
This paper addresses the challenge of determining optimal cut-offs for a set of n items with m scores to maximize distinguishability. The term distinguishability is defined as the fraction of item pairs assigned to different buckets, where…
We study the problem of predicting a set or list of options under knapsack constraint. The quality of such lists are evaluated by a submodular reward function that measures both quality and diversity. Similar to DAgger (Ross et al., 2010),…
We consider a linear inverse problem whose solution is expressed as a sum of two components: one smooth and the other sparse. This problem is addressed by minimizing an objective function with a least squares data-fidelity term and a…
We consider the convex quadratic optimization problem with indicator variables and arbitrary constraints on the indicators. We show that a convex hull description of the associated mixed-integer set in an extended space with a quadratic…
We generalize the polynomial-time solvability of $k$-\textsc{Diverse Minimum s-t Cuts} (De Berg et al., ISAAC'23) to a wider class of combinatorial problems whose solution sets have a distributive lattice structure. We identify three…
Polytope numbers for a polytope are a sequence of nonnegative integers that are defined by the facial information of a polytope. Every polygon is triangulable and a higher dimensional analogue of this fact states that every polytope is…
Many combinatorial optimization problems such as the bin packing and multiple knapsack problems involve assigning a set of discrete objects to multiple containers. These problems can be used to model task and resource allocation problems in…
The Knapsack Problem is a classic problem in combinatorial optimisation. Solving these problems may be computationally expensive. Recent years have seen a growing interest in the use of deep learning methods to approximate the solutions to…
With the goal of obtaining strong relaxations for binary polynomial optimization problems, we introduce the pseudo-Boolean polytope defined as the convex hull of the set of binary points satisfying a collection of equations containing…
Stochastic dynamic matching problems have recently gained attention in the stochastic-modeling community due to their diverse applications, such as supply-chain management and kidney exchange programs. In this paper, we study a matching…
0-1 knapsack is of fundamental importance in computer science, business, operations research, etc. In this paper, we present a deep learning technique-based method to solve large-scale 0-1 knapsack problems where the number of products…
We consider the framework of convex high dimensional stochastic control problems, in which the controls are aggregated in the cost function. As first contribution, we introduce a modified problem, whose optimal control is under some…
We present filling as a new type of spatial subdivision problem that is related to covering and packing. Filling addresses the optimal placement of overlapping objects lying entirely inside an arbitrary shape so as to cover the most…
An important goal in algorithm design is determining the best running time for solving a problem (approximately). For some problems, we know the optimal running time, assuming certain conditional lower bounds. In this work, we study the…
The paper focuses on a new class of combinatorial problems which consists in restructuring of solutions (as sets/structures) in combinatorial optimization. Two main features of the restructuring process are examined: (i) a cost of the…
In this paper we apply the multicanonical method of statistical physics on the number-partitioning problem (NPP). This problem is a basic NP-hard problem from computer science, and can be formulated as a spin-glass problem. We compute the…
In the knapsack problem under explorable uncertainty, we are given a knapsack instance with uncertain item profits. Instead of having access to the precise profits, we are only given uncertainty intervals that are guaranteed to contain the…